Lattice structure of pseudorandom sequences from shift-register generators

Shu Tezuka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)


The author develops a theory of the lattice structure of pseudorandom sequences from shift register generators, i.e., Tausworthe sequences and GFSR (generalized feedback shift register) sequences. The author defines an analog of linear congruential sequences in GF{2,x}, the field of all Laurent series over the Galois field of two elements GF(2), and shows that this class of sequences contains as a subclass the Tausworthe sequence. He derives a theorem that links the k-distribution of such sequences and the successive minima of the k-dimensional lattice over GF{2,x} associated with the sequences, thereby leading to the geometric interpretation of the lattice structure in the k-dimensional unit space of these sequences. This result is generalized to define the successive minima for the point set of k-dimensional vectors each consisting of k consecutive terms of GFSR sequences, and it is shown that GFSR sequences have a similar structure to that of Tausworthe sequences. A simulation problem in which shift-register-type pseudorandom sequences yield useless results due to such lattice structures is discussed.

Original languageEnglish
Title of host publication90 Winter Simulation Conf.
PublisherPubl by IEEE
Number of pages2
ISBN (Print)0911801723
Publication statusPublished - Dec 1990
Event1990 Winter Simulation Conference Proceedings - New Orleans, LA, USA
Duration: Dec 9 1990Dec 12 1990

Publication series

NameWinter Simulation Conference Proceedings
ISSN (Print)0275-0708


Other1990 Winter Simulation Conference Proceedings
CityNew Orleans, LA, USA

All Science Journal Classification (ASJC) codes

  • Software
  • Modelling and Simulation
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety
  • Applied Mathematics


Dive into the research topics of 'Lattice structure of pseudorandom sequences from shift-register generators'. Together they form a unique fingerprint.

Cite this